Question: Simplify the following expression: $ q = \dfrac{-4t - 3}{3t + 2} - \dfrac{-9}{5} $
In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{5}{5}$ $ \dfrac{-4t - 3}{3t + 2} \times \dfrac{5}{5} = \dfrac{-20t - 15}{15t + 10} $ Multiply the second expression by $\dfrac{3t + 2}{3t + 2}$ $ \dfrac{-9}{5} \times \dfrac{3t + 2}{3t + 2} = \dfrac{-27t - 18}{15t + 10} $ Therefore $ q = \dfrac{-20t - 15}{15t + 10} - \dfrac{-27t - 18}{15t + 10} $ Now the expressions have the same denominator we can simply subtract the numerators: $q = \dfrac{-20t - 15 - (-27t - 18) }{15t + 10} $ Distribute the negative sign: $q = \dfrac{-20t - 15 + 27t + 18}{15t + 10}$ $q = \dfrac{7t + 3}{15t + 10}$